The present invention relates in general to digital filters and in particular to a method and apparatus for correcting distortion of signals by analog linear systems.
Digitizing systems, such as digital oscilloscopes, typically use a linear amplifier to amplify (or attenuate) and/or offset an input signal so that the amplifier output signal has peak amplitudes suitably near, but within the full scale input range of a digitizer. This is done so that the input signal can be digitized with full resolution of the digitizer. Unfortunately, due to inherent response characteristics of the amplifier, the output signal produced by an amplifier is a somewhat distorted version of the input signal. For example, When the input signal to an amplifier is a square wave, the resulting "square wave" output signal of the amplifier may be overdamped or underdamped. Thus a waveform data sequence produced by the digitizer in response to an amplifier output signal may not accurately represent a scaled version of the amplifier input signal.
In such digitizing systems, distortion effects of the amplifier can be removed from the waveform data sequence by passing the data sequence through a compensating digital filter such as a finite impulse response (FIR) filter. An FIR filter produces an output data sequence wherein each element is a weighted sum of preceding elements of an input data sequence as represented by the expression: ##EQU1## where x.sub.i is the i.sup.th element of the filter's input data sequence, the first element of the input data sequence being x.sub.0, y.sub.i is the i.sup.th element of the filter's output data sequence, f.sub.n is a weighting factor, and N is the "length" of the filter (i.e., the maximum number of terms in the sum forming each element y.sub.i. The transfer function of such an FIR filter is adjusted by changing the weighting factors f.sub.1, f.sub.2 . . . f.sub.N. A desired transfer function can often be approximated more accurately by increasing the number N of terms in the expression.
While an appropriately adjusted FIR filter can correct a data sequence output of a digitizer to compensate for signal distortion in an analog input signal to the digitizer generated by a linear amplifier, the FIR filter itself introduces distortion. Since elements x.sub.i of the filter's input data sequence for i&lt;0 are not provided to the filter, the filter must compute elements y.sub.i for i&lt;N in accordance with the above expression by assuming arbitrary values such as 0 for x.sub.i when i&lt;0. Since the assumed arbitrary values may bear no relation to magnitudes of the amplifier input signal, the first N-1 terms of the filter output provide a distorted representation of the input signal.